Federated Learning Using Three-Operator ADMM

Federated learning (FL) has emerged as an instance of distributed machine learning paradigm that avoids the transmission of data generated on the users' side. Although data are not transmitted, edge devices have to deal with limited communication bandwidths, data heterogeneity, and straggler effects due to the limited computational resources of users' devices. A prominent approach to overcome such difficulties is FedADMM, which is based on the classical two-operator consensus alternating direction method of multipliers (ADMM). The common assumption of FL algorithms, including FedADMM, is that they learn a global model using data only on the users' side and not on the edge server. However, in edge learning, the server is expected to be near the base station and have direct access to rich datasets. In this paper, we argue that leveraging the rich data on the edge server is much more beneficial than utilizing only user datasets. Specifically, we show that the mere application of FL with an additional virtual user node representing the data on the edge server is inefficient. We propose FedTOP-ADMM, which generalizes FedADMM and is based on a three-operator ADMM-type technique that exploits a smooth cost function on the edge server to learn a global model parallel to the edge devices. Our numerical experiments indicate that FedTOP-ADMM has substantial gain up to 33\% in communication efficiency to reach a desired test accuracy with respect to FedADMM, including a virtual user on the edge server.

EVM Mitigation with PAPR and ACLR Constraints in Large-Scale MIMO-OFDM Using TOP-ADMM

Although signal distortion-based peak-to-average power ratio (PAPR) reduction is a feasible candidate for orthogonal frequency division multiplexing (OFDM) to meet standard/regulatory requirements, the error vector magnitude (EVM) stemming from the PAPR reduction has a deleterious impact on the performance of high data-rate achieving multiple-input multiple-output (MIMO) systems. Moreover, these systems must constrain the adjacent channel leakage ratio (ACLR) to comply with regulatory requirements. Several recent works have investigated the mitigation of the EVM seen at the receivers by capitalizing on the excess spatial dimensions inherent in the large-scale MIMO that assume the availability of perfect channel state information (CSI) with spatially uncorrelated wireless channels. Unfortunately, practical systems operate with erroneous CSI and spatially correlated channels. Additionally, most standards support user-specific/CSI-aware beamformed and cell-specific/non-CSI-aware broadcasting channels. Hence, we formulate a robust EVM mitigation problem under channel uncertainty with nonconvex PAPR and ACLR constraints catering to beamforming/broadcasting. To solve this formidable problem, we develop an efficient scheme using our recently proposed three-operator alternating direction method of multipliers (TOP-ADMM) algorithm and benchmark it against two three-operator algorithms previously presented for machine learning purposes. Numerical results show the efficacy of the proposed algorithm under imperfect CSI and spatially correlated channels.

A Learning-Based Approach to Address Complexity-Reliability Tradeoff in OS Decoders

In this paper, we study the tradeoffs between complexity and reliability for decoding large linear block codes. We show that using artificial neural networks to predict the required order of an ordered statistics based decoder helps in reducing the average complexity and hence the latency of the decoder. We numerically validate the approach through Monte Carlo simulations.

Deep unfolding of the weighted MMSE beamforming algorithm

Downlink beamforming is a key technology for cellular networks. However, computing the transmit beamformer that maximizes the weighted sum rate subject to a power constraint is an NP-hard problem. As a result, iterative algorithms that converge to a local optimum are used in practice. Among them, the weighted minimum mean square error (WMMSE) algorithm has gained popularity, but its computational complexity and consequent latency has motivated the need for lower-complexity approximations at the expense of performance. Motivated by the recent success of deep unfolding in the trade-off between complexity and performance, we propose the novel application of deep unfolding to the WMMSE algorithm for a MISO downlink channel. The main idea consists of mapping a fixed number of iterations of the WMMSE algorithm into trainable neural network layers, whose architecture reflects the structure of the original algorithm. With respect to traditional end-to-end learning, deep unfolding naturally incorporates expert knowledge, with the benefits of immediate and well-grounded architecture selection, fewer trainable parameters, and better explainability. However, the formulation of the WMMSE algorithm, as described in Shi et al., is not amenable to be unfolded due to a matrix inversion, an eigendecomposition, and a bisection search performed at each iteration. Therefore, we present an alternative formulation that circumvents these operations by resorting to projected gradient descent. By means of simulations, we show that, in most of the settings, the unfolded WMMSE outperforms or performs equally to the WMMSE for a fixed number of iterations, with the advantage of a lower computational load.

Dempster-Shafer clustering using Potts spin mean field theory

In this article we investigate a problem within Dempster-Shafer theory where 2**q - 1 pieces of evidence are clustered into q clusters by minimizing a metaconflict function, or equivalently, by minimizing the sum of weight of conflict over all clusters. Previously one of us developed a method based on a Hopfield and Tank model. However, for very large problems we need a method with lower computational complexity. We demonstrate that the weight of conflict of evidence can, as an approximation, be linearized and mapped to an antiferromagnetic Potts Spin model. This facilitates efficient numerical solution, even for large problem sizes. Optimal or nearly optimal solutions are found for Dempster-Shafer clustering benchmark tests with a time complexity of approximately O(N**2 log**2 N). Furthermore, an isomorphism between the antiferromagnetic Potts spin model and a graph optimization problem is shown. The graph model has dynamic variables living on the links, which have a priori probabilities that are directly related to the pairwise conflict between pieces of evidence. Hence, the relations between three different models are shown.